/****************************************************************************
 * Copyright (C) 2009-2010 SciTouch LLC
 * 
 * This file is part of Indigo toolkit.
 * 
 * This file may be distributed and/or modified under the terms of the
 * GNU General Public License version 3 as published by the Free Software
 * Foundation and appearing in the file LICENSE.GPL included in the
 * packaging of this file.
 * 
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 ***************************************************************************/

#include "graph/skew_symmetric_flow_finder.h"

#include "graph/skew_symmetric_network.h"

SkewSymmetricFlowFinder::SkewSymmetricFlowFinder 
   (const SkewSymmetricNetwork &network)
   : _network(network),
   TL_CP_GET(_arc_values), 
   TL_CP_GET(_arc_sym),
   TL_CP_GET(_edge_used_dir),
   TL_CP_GET(_vertex_is_used)
{
   _init();
}

void SkewSymmetricFlowFinder::process ()
{
   QS_DEF(Array<int>, path);
   while (_findAugmentatingPath(path))
      _increaseFlowByPath(path);
}

int SkewSymmetricFlowFinder::getArcValue (int arc) const
{
   return _arc_values[arc];
}

void SkewSymmetricFlowFinder::_init ()
{
   int n_edges = _network.g().edgeEnd();
   _arc_sym.clear_resize(n_edges);
   _arc_values.clear_resize(n_edges);
   _edge_used_dir.clear_resize(n_edges);

   for (int i = 0; i < n_edges; i++)
   {
      _arc_sym[i] = 0;
      _arc_values[i] = 0;
      _edge_used_dir[i] = 0;
   }

   for (int e = _network.g().edgeBegin(); 
            e != _network.g().edgeEnd();
            e = _network.g().edgeNext(e))
   {
      _arc_sym[e] = _network.getSymmetricArc(e);
   }

   _vertex_is_used.clear_resize(_network.g().vertexEnd());
   for (int i = 0; i < _vertex_is_used.size(); i++)
      _vertex_is_used[i] = 0;

   _network_sink = _network.getSymmetricVertex(_network.getSource());
}

bool SkewSymmetricFlowFinder::_findAugmentatingPath (Array<int> &vertices)
{
   for (int i = 0; i < _vertex_is_used.size(); i++)
      _vertex_is_used[i] = 0;
   for (int i = 0; i < _edge_used_dir.size(); i++)
      _edge_used_dir[i] = 0;

   vertices.clear();
   vertices.push(_network.getSource());
   return _findAugmentatingPathRec(vertices);
}

bool SkewSymmetricFlowFinder::_findAugmentatingPathRec (Array<int> &vertices)
{
   // This is trivial implementation that takes exponential time in worth case
   // There is fast polynomial algorithm bud trimming algorithm that 
   // will be implemented in future

   int from = vertices.top();
   if (from == _network_sink)
      return true;

   _vertex_is_used[from] = 1;
   const Vertex &v = _network.g().getVertex(from);
   for (int i = v.neiBegin(); i != v.neiEnd(); i = v.neiNext(i))
   {
      int edge = v.neiEdge(i);
      int edge_sym = _network.getSymmetricArc(edge);

      int nei_vertex = v.neiVertex(i);
      if (_vertex_is_used[nei_vertex])
         continue;

      if (_isEdgeAugmentating(edge, from, _edge_used_dir[edge_sym]))
      {
         vertices.push(v.neiVertex(i));

         if (_network.getArcType(edge, from) == ARC_OUT)
            _edge_used_dir[edge] = 1;
         else
            _edge_used_dir[edge] = -1;

         bool ret = _findAugmentatingPathRec(vertices);
         if (ret)
            return true;
         _edge_used_dir[edge] = 0;
         vertices.pop();
      }
   }
   _vertex_is_used[from] = 0;
   return false;
}

int SkewSymmetricFlowFinder::_getResidualCapacity (int edge, int from)
{
   if (_network.getArcType(edge, from) == ARC_OUT)
   {
      // Outgoing arc
      return _arc_values[edge];
   }
   else
   {
      // Incomming arc
      return _network.getArcCapacity(edge) - _arc_values[edge];
   }
}

bool SkewSymmetricFlowFinder::_isEdgeAugmentating (int edge, int from, int sym_used_dir)
{
   int residual_capacity = _getResidualCapacity(edge, from);
   int delta = _network.getArcCapacity(edge) - residual_capacity;

   int edge_dir_cur;
   if (_network.getArcType(edge, from) == ARC_OUT)
      edge_dir_cur = 1;
   else
      edge_dir_cur = -1;

   if (edge_dir_cur * sym_used_dir == -1)
      return 0; // This edge will be changed by 0

   if (sym_used_dir != 0 && delta > 1)
      return true;
   if (sym_used_dir == 0 && delta > 0)
      return true;
   return false;
}

void SkewSymmetricFlowFinder::_increaseFlowByPath (Array<int> &vertices)
{
   int delta = -1;
   // Find path maximum delta
   for (int i = 1; i < vertices.size(); i++)
   {
      int from = vertices[i - 1];
      int to = vertices[i];
      int edge = _network.g().findEdgeIndex(from, to);
      int edge_sym = _network.getSymmetricArc(edge);

      int cur_delta = _network.getArcCapacity(edge) - 
         _getResidualCapacity(edge, from);

      if (_edge_used_dir[edge_sym] != 0)
      {
         if (_edge_used_dir[edge_sym] * _edge_used_dir[edge] == 1)
            cur_delta = cur_delta / 2;
         else
            continue; // Delta for this edge is zero
      }

      if (delta == -1 || delta > cur_delta)
         delta = cur_delta;
   }
   if (delta == 0)
      throw Error("algorithm error: delta should be positive");

   // Update network flow
   for (int i = 1; i < vertices.size(); i++)
   {
      int from = vertices[i - 1];
      int to = vertices[i];
      int edge = _network.g().findEdgeIndex(from, to);
      int edge_sym = _arc_sym[edge];

      int cur_delta = delta;

      if (_edge_used_dir[edge_sym] != 0)
      {
         if (_edge_used_dir[edge_sym] * _edge_used_dir[edge] == -1)
            continue; // Delta for this edge is zero
      }

      if (_edge_used_dir[edge] == -1)
         cur_delta = -cur_delta;

      _arc_values[edge] += cur_delta;
      _arc_values[edge_sym] += cur_delta;
   }

   // For debug purposes
   _dbgCheckConsistency();
}

void SkewSymmetricFlowFinder::_dbgCheckConsistency ()
{
   // Check that all arc values are in bounds
   const Graph &g = _network.g();
   for (int e = g.edgeBegin(); e != g.edgeEnd(); e = g.edgeNext(e))
   {
      if (_arc_values[e] < 0 || _arc_values[e] > _network.getArcCapacity(e))
         throw Error("arc values are not in bounds");

      int se = _arc_sym[e];
      if (_arc_values[e] != _arc_values[se])
         throw Error("symmetry arc values are not the same");
   }

   // Check divergence
   int source_div = -1, sink_div = -1;
   for (int v = g.vertexBegin(); v != g.vertexEnd(); v = g.vertexNext(v))
   {
      int div = 0;
      const Vertex &vert = g.getVertex(v);
      for (int nei = vert.neiBegin(); nei != vert.neiEnd(); nei = vert.neiNext(nei))
      {
         int e = vert.neiEdge(nei);
         if (_network.getArcType(e, v) == ARC_OUT)
            div += _arc_values[e];
         else
            div -= _arc_values[e];
      }

      if (v == _network_sink)
         sink_div = div;
      else if (v == _network.getSource())
         source_div = div;
      else if (div != 0)
         throw Error("internal vertex divergence must be zero");
   }

   if (source_div + sink_div != 0)
      throw Error("source and sink Divergence must be zero in sum");
}
